Back مجسم المعين المنحرف Arabic Trapezoeder German Kajtopluredro Esperanto Trapezoedro Spanish Trapezoedro Basque Trapetsoedri Finnish Antidiamant French Trapezoedro IO Trapezoedro Italian ねじれ双角錐 Japanese
| Set of dual-uniform n-gonal trapezohedra | |
|---|---|
 Example: dual-uniform pentagonal trapezohedron (n = 5) | |
| Type | dual-uniform in the sense of dual-semiregular polyhedron |
| Faces | 2n congruent kites |
| Edges | 4n |
| Vertices | 2n + 2 |
| Vertex configuration | V3.3.3.n |
| Schläfli symbol | { } ⨁ {n}[1] |
| Conway notation | dAn |
| Coxeter diagram |     |
| Symmetry group | Dnd, [2+,2n], (2*n), order 4n |
| Rotation group | Dn, [2,n]+, (22n), order 2n |
| Dual polyhedron | (convex) uniform n-gonal antiprism |
| Properties | convex, face-transitive, regular vertices[2] |
In geometry, an n-gonal trapezohedron, n-trapezohedron, n-antidipyramid, n-antibipyramid, or n-deltohedron[3],[4] is the dual polyhedron of an n-gonal antiprism. The 2n faces of an n-trapezohedron are congruent and symmetrically staggered; they are called twisted kites. With a higher symmetry, its 2n faces are kites (sometimes also called trapezoids, or deltoids).[5]
The "n-gonal" part of the name does not refer to faces here, but to two arrangements of each n vertices around an axis of n-fold symmetry. The dual n-gonal antiprism has two actual n-gon faces.
An n-gonal trapezohedron can be dissected into two equal n-gonal pyramids and an n-gonal antiprism.
- ^ N.W. Johnson: Geometries and Transformations, (2018) ISBN 978-1-107-10340-5 Chapter 11: Finite symmetry groups, 11.3 Pyramids, Prisms, and Antiprisms, Figure 11.3c
- ^ "duality". maths.ac-noumea.nc. Retrieved 2020-10-19.
- ^ Weisstein, Eric W. "Trapezohedron". MathWorld. Retrieved 2024-04-24. Remarks: the faces of a deltohedron are deltoids; a (non-twisted) kite or deltoid can be dissected into two isosceles triangles or "deltas" (Δ), base-to-base.
- ^ Weisstein, Eric W. "Deltahedron". MathWorld. Retrieved 2024-04-28.
- ^ Spencer 1911, p. 575, or p. 597 on Wikisource, CRYSTALLOGRAPHY, 1. CUBIC SYSTEM, TETRAHEDRAL CLASS, footnote: « [Deltoid]: From the Greek letter δ, Δ; in general, a triangular-shaped object; also an alternative name for a trapezoid ». Remark: a twisted kite can look like and even be a trapezoid.